1. Field of the Invention
The present invention relates to a method of suppressing geometric distortions contained in an image space, for example, when a plane shape is measured based on an image that is taken by an imaging device such as a CCD camera from a sample space to be measured.
2. Description of the Related Art
Conventional methods of compensating geometric distortions occurred in an image space imaged by a CCD camera, for example, through the use of grid-like graphics as a reference space, include:
(1) a method of approximating with divisional polynomials;
(2) a method of executing affine transformations over the entire space; and
(3) a method of functionally approximating through the step of searching for reasons that cause distortions such as aberration on lens.
The method (1), which approximates using divisional polynomials, can be expected to achieve a high precision through the use of higher order polynomials, which on the other hand elevates a computational cost. The method (2), which executes affine transformations over the entire space, is not possible to respond non-linear distortions and thus can not be expected to achieve a high precision. The method (3), which functionally approximates, is difficult to derive a function and can not be expected to achieve a high precision for such a distortion that greatly varies a local curvature.
Accordingly, there is no practical method in the art that is possible to compensate distortions in an image space easily within any designated tolerance.
An object of the present invention is to provide a method capable of suppressing geometric distortions in an image space easily within a predetermined tolerance.
The present invention is provided with a method of suppressing geometric distortions in an image space obtained by imaging a sample space to be measured. The method comprises the steps of: preparing a reference space correspondingly located to a sample space to be measured, the reference space including a plurality of reference graphics and having previously known coordinate value positions of every graphic cores in the reference graphics and of a reference center defined as a graphic core of the whole reference graphics in the reference space; superimposing a transcription center in an image space on the reference center in the reference space, the image space being obtained by imaging the sample space to include a plurality of imaged graphics corresponding to the plurality of reference graphics, the transcription center being defined as a graphic core of the whole imaged graphics in the image space; executing a primary affine transformation to transform a group of transcription graphic cores consisting of graphic cores in the plurality of imaged graphics, core-by-core, on a group of reference graphic cores consisting of graphic cores in the plurality of reference graphics; performing a primary spatial division to divide the reference space into a plurality of primarily divided spaces; deriving an estimation of distortion for each of the primarily divided spaces from a positional error between each transcription graphic core after the primary affine transformation and the corresponding reference graphic core; classifying the primarily divided spaces into in- and out-of-tolerance divided spaces having estimation of distortion falling inside and outside a predetermined tolerance; executing a secondary affine transformation for the out-of-tolerance divided spaces to transform a group of transcription graphic cores in the corresponding image space on a group of reference graphic cores in the out-of-tolerance divided spaces; performing a secondary spatial division to divide the out-of-tolerance primarily divided spaces into a plurality of secondarily divided spaces after the primary and secondary affine transformations; and repeating affine transformations and spatial divisions for the out-of-tolerance divided spaces until the estimation of distortion fall inside the predetermined tolerance.
According to the present invention, repetitions of affine transformations and spatial divisions can easily eliminate geometric distortions in an image space obtained through imaging a sample space to be measured by means of a CCD camera or the like.
In the method of the present invention, the estimation of distortion may be determined as the maximum of a norm for a positional error between the reference graphic core and the transcription graphic core after the affine transformation. Alternatively, if the nearest transcription graphic core from the reference graphic core can be obtained, the estimation of distortion may be determined as the maximum of a norm for a positional error between the nearest transcription graphic core and the transcription graphic core corresponding to the reference graphic core. In each of the affine transformations, an affine transformer may be determined through the use of the least mean-square method for a positional error between a transformed position and the corresponding reference graphic core. Each of the spatial divisions may comprise a four-part division by dividing a space vertically and horizontally each in approximately two. The plurality of reference graphics may locate reference graphic cores thereof partly on a boundary of either the reference space or each of divided spaces obtained by dividing the reference space. A boundary of either the reference space or each of reference regions obtained by dividing the reference space may describe either one of a rectangle, triangle or circular arc.